Meaning-Game-based Centering Modelwith Statistical Definition of Utility of Referential Expression
and Its Verification Using Japanese and English Corpora
Shun Shiramatsu∗ , Kazunori Komatani∗ , Kôiti Hasida† , Tetsuya Ogata∗ , Hiroshi G. Okuno∗∗

Graduate School of Informatics, Kyoto University
Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan{siramatu, komatani, ogata, okuno}@kuis.kyoto-u.ac.jp†
ITRI, National Institute of Advanced Industrial Science and Technology (AIST)
Akihabara Dai-Building, Soto-Kanda 1-18-13, Chiyoda-ku, Tokyo 101-0021, Japan
hasida.k@aist.go.jp
Abstract
This paper presents a quantitative modeling of referential coherence by which conversation systems measure the smoothness of discourse.
Investigations of the corpora show that referential coherence depends on languages or genres of discourse. Our goal is to establish
a quantitative model that can be statistically adapted to various languages. Centering theory explains referential coherence by using
heuristic rules. Since these heuristics should be invented manually for a particular language, we need a quantitative/statistical model thatcan be obtained from a corpus. The meaning-game-based centering model (MGCM) (Shiramatsu et al., 2005) quantitatively reformulates
centering theory by exploiting quantitative aspects of game theory. It quantifies referential coherence by using the two parameters related
to salience and pronominalization: “reference probability” and “perceptual utility”. However, MGCM still has two problems. The first isthat perceptual utility cannot be statistically adapted to various languages. The second is that MGCM has only been verified in Japanese.
We have enhanced the model by statistically defining perceptual utility. Specifically, we defined it by using occurrence frequency of
the referential expression in a corpus. Experimental results using English and Japanese corpora showed that our statistical definitions
enabled the parameters to be adapted to both corpora. Furthermore, the statistical tests of the enhanced MGCM showed its validity inboth corpora.

1. Introduction
Quantification of referential coherence is important for
conversation systems to be able to automatically measure
the smoothness of generated discourse (e.g., when the system selects a coherent utterance from a number of candidate utterances). Referential coherence can be measured
on the basis of discourse salience and pronominalization.
Referential coherence depends on languages or genres of
discourse, according to investigations of corpora. Our goal
is to formulate a quantitative model of referential coherence with parameters related to salience and pronominalization. We assume that pronominalization can be quantitatively defined as the amount of perceptual load reductionin the interlocutors’ cognitive process. It is desirable thatthe model be applicable to various languages. To adapt themodel to various language corpora, the parameters of themodel should be statistically defined.
Centering theory (CT) (Grosz et al., 1995) is a theoryof discourse salience, anaphora, and referential coherence
based on heuristic rules (e.g., Cf-ranking and transition
ranking). It is useful for estimating referential coherence
between utterance units and for selecting appropriate referential expressions. It does not, however, give a quantitativemodel.
The resolution of anaphora procedure (RAP) (Lappin andLeass, 1994), another approach similar to CT, includes
salience weightings based on Alshawi (1987)’s salience
factors. Although its salience weightings is apparently
quantitative, it is defined as a rule-based weighting with apriori heuristics, without corpus-based statistics.

The meaning-game-based centering model (MGCM)(Shiramatsu et al., 2005) is a quantitative reformulation ofCT, which is derived from game theory. It quantifies referential coherence with a principle of expected utility, whichis game-theoretical hypothesis about the relationship between discourse salience and pronominalization.
Because this principle is not based on the properties ofa specific language, the model can be applied to various
languages. Furthermore, such a quantitative approach canobtain parameters optimized to a target language by statistically analyzing a corpus in that language.
The modeling of MGCM, however, is not fully statistical. Specifically, the perceptual utility of referential expressions, which represents reduction of the perceptual load, ismanually designed. Such a manual approach requires specialized skills to adapt the model to each language. Moreover, such manual adaptation is difficult to justify its accuracy. Due to this imperfection of the methodology of adaptation, the effectiveness of MGCM has so far been verified
only with a Japanese corpus. For verification in other languages, it requires corpus-based statistical design in orderto enable easier and more accurate parameter fitting.
In this paper, we statistically define perceptual utility.
The definition is based on the assumption that higher-utility
words should be costless and frequently used (i.e., morefamiliar) in the target corpus. Furthermore, we verify themodel using both Japanese and English corpora. We quantitatively discuss the difference in pronominalization between Japanese and English corpora.

Table 1: Transition types

Table 2: Correspondence of CT and MGCM
CT
(Non-quantitative)

Cb(Ui+1 ) = Cb(Ui ) Cb(Ui+1 ) 6=Cb(Ui )CONTINUESMOOTH-SHIFT
Cb(Ui+1 ) 6=Cp(Ui+1 )RETAINROUGH-SHIFT
Here, Cp(Ui ), the preferred center of utterance Ui ,is the highest ranked element of Cf(Ui ).
Cb(Ui+1 ) =Cp(Ui+1 )2.

Problems with Conventional Studies

Discourse Cf-ranking
salience(Subject>Object> · · ·)LoadPronominalization
reduction (Pronoun / Non-pronoun)
Referential Transition ranking
coherence (CONTINUE>RETAIN

This section describes the issues of conventional CT and
MGCM.

>SMOOTH-SHIFT

MGCM(Quantitative)
Reference probability
Pr(e|U1 , · · · , Ui )Perceptual utility
Ut(w)Expected utility
EU(UP i+1 )=
Pr(e|U1 , · · · , Ui )Ut(w)w refers to e in Ui+1

>ROUGH-SHIFT)

2.1. Centering Theory
CT handles a discourse as a sequence of utterance units[U1 , U2 , · · · , Un ]. CT explains the referential expression
between Ui+1 and Ui by using heuristics: a salience ranking of grammatical roles (Cf-ranking) (Walker et al., 1994),
three constraints about “center”, and two rules about referential coherence (Poesio et al., 2004).
English Cf-ranking: subject > object > indirect object> complement > adjunctJapanese Cf-ranking: topic (zero or grammatical) >subject > indirect object > object > others
Cb(Ui ): The backword-looking center of Ui .
Cf(Ui ): The forward-looking centers of Ui .
Constraint 1: All utterances of a segment except for the
1st have at most one Cb.
Constraint 2: Every element of Cf(Ui ) must be realizedin Ui .
Constraint 3: Cb(Ui ) is the highest ranked element ofCf(Ui−1 ) that is realized in Ui .
Rule 1 (Pronominalization rule): If any Cf(Ui ) is
pronominalized, Cb(Ui ) is also pronominalized.
Rule 2 (Transition rule): Transition types are ordered: CONTINUE > RETAIN > SMOOTH-SHIFT >ROUGH-SHIFT (See also Table 1).
Different researchers proposed different versions of theabove heuristics. The variations of them, however, do not
clearly specify a principle behind referential coherence represented with Rules 1 and 2. We fear that variations of CT
will disorderly grow without principled background. We
need a simple modeling which explains principled mechanism behind the phenomena.
Moreover, the Cf-ranking requires specialized skills foradapting it to each language. For example, the ordering ofobjects and indirect objects in Japanese is difficult to justify.
We need a methodology for automatic adaptation.
2.2. Meaning-Game-based Centering Model
The meaning game (MG) (Hasida, 1996) is a gametheoretical model of intentional communication. MGCM
(Shiramatsu et al., 2005) is a quantitative reformulation of
CT based on the MG framework. It quantifies referential
coherence with the following two parameters.
• Reference probability (Pr): Probability of a target
entity being referenced in a following utterance unit. It

U1 , · · · , Ui : Preceding discourse
Ui+1 : Following utterance unit

e: Entity referenced in U1 , · · · , Ui
w: Referential expression in Ui+1

Table 3: Features of reference pattern of e used in calculating Pr(e|U1 , · · · , Ui )log ( (# utterances between Ui and the latest
reference to e in [U1 , · · · , Ui ]) + 1)
gram grammatical role of the latest reference to e
in [U1 , · · · , Ui ]chain log ( (# references to e in [U1 , · · · , Ui ]) + 1)
dist

Ui-2: I saw Tom a little while ago.

Ui-2: John bought a piano.

Ui-1: He seemed sleepy.

chain=log(2+1)
Ui-1: It was so expensive.

Ui : It had been so hot last night.

Ui : I can’t believe that.

Ui+1:

Ui+1:

chain=log(2+1)

gram=subject

dist=log(2+1).

Target: (“Tom”, [U1,…,Ui])
Pr(“Tom”|U1,…,Ui) =gram=subject

dist=log(2+1).

Samples having same patternfrom a corpus#Referenced in Ui+1
#Samples having same pattern

Logistic regression is practically used for calculating Pr(e|U1,…,Ui)in order to cope with data sparseness.

Pr(e | U1 ,..., U i ) = (1 + exp(−(b0 + b1dist + b2 gram + b3chain))) −1

Figure 1: Calculation of Pr(e|U1 , · · · , Ui )represents discourse salience, i.e., degree of attention
to the target discourse entity.
• Perceptual utility (Ut): Reduction of perceptual costwhen interlocutors transmit a target referential expression. For example, ellipses and pronouns have higher
perceptual utilities because they are perceptually simple and costless.
Table 2 presents the correspondence between MGCM
and CT. Here, e represents a target entity referenced in apreceding discourse, [U1 , · · · , Ui ]. w represents a referential expression referring to e in the following utterance unit,
Ui+1 .
The reference probability of e, Pr(e|U1 , · · · , Ui ), represents the conditional probability of e being referenced in
Ui+1 , given the reference pattern of e in [U1 , · · · , Ui ] . Table 3 shows the features we used as the reference pattern.
Figure 1 outlines the calculation of the Pr value by using a
corpus. The calculation uses logistic regression analysis inorder to cope with data sparseness. Pr represents the degreeof salience of e at the moment of Ui .

The perceptual utility of w, Ut(w), represents the perceptual load reduction of using the referential expression w.
For example, ellipsis and pronouns have higher utility because their perceptual cost is lower than other noun phrases.
Ut(w) is used for generalizing Rule 1 of CT, which is a rule
about pronominalization.
The expected utility of Ui+1 , EU(Ui+1 ), represents the
expected load reduction when interlocutors output or predict Ui+1 . For example, EU(Ui+1 ) is high when a costless pronoun in Ui+1 refers to a salient entity. It represents the degree of referential coherence between Ui+1 and[U1 , · · · , Ui ].
The principle of MGCM is that referential coherence isachieved by reducing the communicating load for interlocutors, which is represented as the expected utility derived
from game theory. This principle is possibly common tovarious languages; hence MGCM should be applied to thevarious languages in order to find out if this is the case. To
apply it to various languages, two parameters, Pr and Ut,
should be statistically obtained from a corpus of each language.
Shiramatsu et al. (2005) statistically defined reference
probability, Pr, in order to enable corpus-based fitting of Pr.
Perceptual utility, Ut, however, was not statistically defined.
It was naively assumed that a pronoun had higher Ut than a
non-pronoun. A corpus-based statistical definition of Ut isneeded to apply MGCM to other language corpora.
In fact, the effectiveness of the model has so far beenverified only with a Japanese corpus.

3.

Statistical Definition of Perceptual Utility

Perceptual utility represents interlocutors’ perceptualload reduction in transmitting (speaking, writing, hearing,or reading) a lexical symbol of a target referential expression. It does not contain the cost of semantic understanding(e.g., anaphor resolution). Shiramatsu et al. (2005) naively
assumed that pronouns had higher perceptual utilities than
non-pronouns.
We assume that perceptual simplicity can be calculatedusing frequency of referential expressions for the following reasons: Frequent expressions cost less than rare ones
because interlocutors are habituated to frequent ones. Costless expressions are more frequently used than costly ones.
We define the perceptual cost of a target referential expression w as follows:(Perceptual cost of w) = I(w) = − log p(w).
Here, p(w) represents the probability of w appearing as
an anaphoric expression in a corpus. Given this definition,
the perceptual cost of w is calculated with the following
equation:I(w) = − log p(w)#w as anaphoric expressions= − log[nat].
# all utterance units
The perceptual utility is the reverse of the perceptual cost.
We define the perceptual utility of a target referential expression w as follows:(Perceptual utility of w) = Ut(w)= −(perceptual cost of w) + (basic level)= −I(w) + Ut 0 .
The basic level Ut 0 is empirically defined to ensure thatUt(w) > 0.
We propose to replace the definition of perceptual utility
in Shiramatsu et al. (2005) with the new one. We call thisenhanced version “enhanced MGCM” hereafter.

4.

Empirical Verification using Large
Japanese and English Corpora

To verify enhanced MGCM on different languages, weused the Wall Street Journal (hereafter, WSJ) as an English
corpus and the Mainichi-Shinbun (hereafter, Mainichi) asa Japanese corpus. WSJ contains 2,412 articles, 135,278
predicate clauses, and 95,677 anaphors. Mainichi contains 1,356 articles, 63,562 predicate clauses, and 16,728
anaphors. The verification requires linguistic annotations
which specify structure of morpheme, dependency, andanaphora. Both corpora are manually annotated according to Global Document Annotation (GDA) (Hasida, 1998).
The following examples illustrate the GDA tags specifying
the anaphora structures.
<su syn="b"><namep id="Foo">The foo model </namep>should be adaptable to<np id="Data">various data</np>.</su><su syn="b"><adp>However</adp>, <np eq="Foo">it </np>
lacks the methodology for<np obj="Foo" gol="Data">adapting</np>.</su>

Here, the attribute id represents antecedent. The attribute
eq represents anaphor except for ellipsis. The relational
attributes obj and gol represent ellipsis.
4.1. Verification of Definition of Discourse Salience
The MGCM statistically defined discourse salience as areference probability Pr(e|U1 , · · · , Ui ). Calculation of Pr(See also Figure 1) required the following two preparations.
Firstly, we needed to assign the gram value to each grammatical role. We assigned Pr average of each grammaticalrole, Pr(gram), which was calculated by counting samples
in Mainichi and WSJ corpora (Tables 4 and 5). Secondly,
we needed to obtain the regression weights bi from the corpora. We obtained bi by logistic regression analysis (Table
6). We used 12,000 subsamples from corpora per one trialof the logistic regression analysis.
Tables 4 and 5 show the consistency between Pr(gram)
ranking and the conventional Cf-ranking. The Pr order in
Mainichi among “Topic,” “Subject,” and “Object” was consistent with the conventional Japanese Cf-ranking. The Prorder in WSJ among ”Subject,” “Object,” and “Complement” was also consistent with the conventional English
Cf-ranking. These consistencies indicate the validity of thePr definition in the both corpora.
Tables 4 and 5 also illustrate the difference between
Mainichi and WSJ. Although they were similar in the Prorder between “Subject” and “Object”, they were different
in the distributions of Pr value. This indicates that Pr wasTable 4: Reference probability for each grammatical role
(Mainichi, Japanese corpus)

Table 7: Perceptual cost of each referential expression(Mainichi, Japanese corpus)

Type of gram
# Samples # Referenced Pr(gram)
Topic (wa)35,3291,908 5.40×10−2
Subject (ga)38,4501,107 2.88×10−2(no)88,695
1,755 1.98×10−2
Object (o)50,217898 1.79×10−2
Indirect object (ni)46,058569 1.24×10−2
(mo)
8,710
105 1.21×10−2(de)
24,142267 1.11×10−2(kara)
7,963
76 9.54×10−3(to)
19,383
129 6.66×10−3

Referential expression Appearance probability Perceptual costw
p(w)
I(w) [nat](Zero pronoun)
2.940 × 10−1
1.224
watashi (I)5.129 × 10−3
5.273
sono (that)
3.965 × 10−3
5.530
kore (this)2.973 × 10−3
5.818
kono (this)1.888 × 10−3
6.272
Nihon (Japan)
1.809 × 10−3
6.315
mono (thing)1.809 × 10−3
6.315
..
..
..
.
.
.

Table 5: Reference probability for each grammatical role
(WSJ, English corpus)
Type of gram # Samples # Referenced Pr(gram)
Subject
76,147
16,441 2.16×10−1
(by)
5,045
618 1.22×10−1
Indirect object
1,569
184 1.17×10−1(with)
4,272
446 1.04×10−1(of)
23,7982,145 9.01×10−2(from)
4,005
350 8.74×10−2
Object42,5783,703 8.70×10−2
(to)
8,449
661 7.82×10−2
(for)
7,759
601 7.75×10−2
(on)
5,140
229 5.82×10−2
(at)
4,043
233 5.76×10−2
Complement
7,102
371 5.22×10−2

Table 6: Regression weights in logistic regression for Pr
Corpus b0 (Const.) b1 (dist)
Mainichi-2.825-0.7636
WSJ-2.405-1.411b2 (gram)
9.036
8.788

b3 (chain)
2.048
3.519

Type of w
Zero pronoun
PronounOther noun

Average of p(w)2.940 × 10−1
2.403 × 10−3
2.271 × 10−4

Perceptual cost
1.224
6.031
8.390

Table 8: Perceptual cost of each referential expression(WSJ, English corpus)
Referential expression Appearance probability Perceptual costw
p(w)
I(w) [nat](Empty category)
2.547 × 10−1
1.368
it
4.232 × 10−2
3.162
he
3.049 × 10−2
3.490
they
1.850 × 10−2
3.990
company
1.652 × 10−2
4.103
we
1.112 × 10−2
4.499
I1.020 × 10−2
4.585
U.S.
8.342 × 10−3
4.786
..
..
..
.
.
.
Type of w
Empty category
PronounOther noun

Average of p(w)2.457 × 10−1
3.257 × 10−2
1.317 × 10−3

Perceptual cost
1.368
3.836
6.632

fitted to each corpus. Additionally, the difference is due tolanguage difference in the types of grammatical roles. This
also indicates the necessity of corpus-based parameter fittings for each language.
Table 6 shows the consistency between the regression
weights obtained from the corpora and linguistic heuristics.
The negative values of the weight of dist, b1 , are consistent
with the heuristics that the recently referenced entities are
more salient than the earlier ones. The positive values of theweight of gram, b2 , are consistent because Pr(gram) represents salience of each grammatical role. The positive valuesof the weight of chain, b3 , are consistent with the heuristics
that the frequently referenced entities are more salient than
the rare ones. These consistencies in both corpora indicatethat the adaptation to the corpora is successful by logistic
regression analysis. These also indicate the validity of thePr definition in both corpora.

age costs for ellipsis, pronoun, and other nouns. In both
corpora, the rankings of the categories were consistent withthe heuristics as follows:
Ellipsis < Pronoun < Other nouns
These results justify the validity of our definition in both
Mainichi and WSJ.
Tables 7 and 8 also show the difference between Mainichi
and WSJ. Although they were similar, the distributions weredifferent due to language difference in the types of referential expressions. This indicates that Ut was fitted to each
corpus. It also indicates the necessity of corpus-based parameter fitting to each language.

4.2. Verification of Definition of Perceptual Cost
The enhanced MGCM statistically defines the perceptual
cost as I(w), the amount of self-information. We therefore
measured I(w) for each referential expression w. Tables 7
and 8 show the rankings of referential expressions in orderof perceptual cost.
An ellipsis (zero pronoun or empty category) has the lowest cost in both corpora. Pronouns (in colored rows in thetables) tend to have lower cost than non-pronouns in both
corpora. The lower three rows in the tables list the aver-• Preference 1a: w1 refers to e1 and w2 refers to
e2 when Pr(e1 |U1 , · · · , Ui ) > Pr(e2 |U1 , · · · , Ui ) andUt(w1 ) > Ut(w2 ), given that (w1 , w2 ) is a pair ofanaphor in Ui+1 (Figure 2).

4.3. Verification of Preferences in
Meaning-Game-based Centering Model
MGCM contains Preferences 1a, 1b, and 2, which are
general formulations of Rules 1 and 2 of CT (Shiramatsu etal., 2005).

• Preference 1b: There is a positive correlation between Pr(e|U1 , · · · , Ui ) and Ut(w), given that w refers
to e in Ui+1 (Figure 2).

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Figure 2: EU(Ui+1 ) increases through positive correlation
between Pr and Ut (Preferences 1a and 1b).
• Preference 2: The higher EU(Ui+1 ) is preferred.
Preference 2 is the principle of MGCM derived fromgame theory. It is a generalization of Rule 2 of CT (i.e.,transition rule). Preference 1a is derived from Preference 2(See also Figure 2). Preference 1b is derived from Preference 1a. Preferences 1a and 1b are generalizations of Rule
1 of CT (i.e., pronominalization rule).
As preparation of verification, we had to determine thevalue of Ut 0 , the basic level of Ut. We empirically determined that Ut 0 = 12[nat]. The grounds for this setting aredescribed in the discussion section.
Verification of Preference 1a: We measured the ratio ofsamples which comply with Preference 1a (i.e., (A) in Figure 2) in order to verify Preference 1a. The ratio is influenced by differences in Pr and Ut between w1 and w2 , i.e.,∆Pr = logPr(e1 ) − logPr(e2 ) and ∆Ut = Ut(w1 ) −Ut(w2 ). The greater the differences, the larger the ratio of
the compliant samples.
We varied a threshold of ∆Pr and ∆Ut to investigate
the influence of ∆Pr and ∆Ut. We applied Preference 1a
to samples only in range that ∆Pr and ∆Ut were greaterthan a certain threshold. Here, we took the ratio of in-range
compliant samples to all compliant samples as the recallof Preference 1a. We took the ratio of in-range compliant
samples to all in-range samples as the precision of Preference 1a. Figure 3 shows the recall-precision curve by thethreshold varying. When the recall was 100%, the precision
was greater than 60% on both corpora. When the recall
was 60%, the precision was approximately 70% on both.
These results indicate the validity of Preference 1a because
the precisions are always greater than 60% over the whole
range.
Verification of Preference 1b: We verified Preference
1b, i.e., the positive correlation between Pr and Ut. The
correlation coefficient in Mainichi is greater than +0.356
at the 2.5% significance level. That in WSJ is greater than
+0.217 at the 2.5% significance level. Therefore, Preference 1b was statistically significant in both corpora because
the positive correlation was statistically significant.

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(Mainichi, Japanese corpus)
Transition type

Samples

Average of EU(Ui+1 )CONTINUERETAINSMOOTH-SHIFTROUGH-SHIFT

1,783
84
2,704
194

10.374
7.913
2.624
1.428

Table 10: Average of EU(Ui+1 ) for each transition type
(WSJ, English corpus)
Transition type

Samples

Average of EU(Ui+1 )CONTINUERETAINSMOOTH-SHIFTROUGH-SHIFT

13,384
2,314
18,904
5,628

5.439
3.295
2.664
1.031

Verification of Preference 2: We verified the consistency
between the expected utility, EU(Ui+1 ), of MGCM and thetransition ranking, i.e., Rule 2 of CT. As preparation, we
determined the transition types of samples in corpora byusing Pr values as a substitute for the Cf-rankings.
Tables 9 and 10 show the consistency of ranking by average expected utility of MGCM with the transition rankingof CT. Wilcoxon’s rank sum test was statistically significant on both corpora at the 99% confidence level. Therefore, Preference 2 was statistically significant in Mainichi
and WSJ.
Furthermore, we investigated the correlation coefficient
between the transition ranking and EU(Ui+1 ). As preparation, we assigned the ranked values according to transition
ranking of CT: CONTINUE: 4, RETAIN: 3, SMOOTHSHIFT: 2, and ROUGH-SHIFT: 1. As the result, the correlation coefficient in Mainichi was equal to +0.585. That in
WSJ was equal to +0.407. These results also provide statistical evidence for the validity of EU(Ui+1 ) as a scale of thereferential coherence between Ui+1 and [U1 , · · · , Ui ].

5.

Discussions

Here, we quantitatively compare Mainichi and WSJ. Additionally, we describe the grounds for the Ut 0 setting.
5.1. Quantitative Comparison of Mainichi and WSJ
Here, we quantitatively compare Mainichi and WSJ fromthe viewpoint of Preference 1b. Although the correlation
coefficients were significantly positive in the both corpora,the coefficient in WSJ was less than that in Mainichi. Figure
5 indicates its reason. It represents the correlation between

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Ut(w) ≥ 0 is not ensured). This result shows that Preference 2 is valid as long as Ut(w) ≥ 0 is ensured. In WSJ,
max I(w) = 11.82. In Mainichi, max I(w) = 11.06 [nat].
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6. Conclusion

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Figure 5: Ratios of pronominalized entities
the Pr value and the ratio of pronominalized entities, i.e.,high-Ut entities. In the range of Pr < 0.75, the ratio of
pronominalized entities increased though the increase of Pr
in both corpora. In the range of Pr > 0.75 (i.e., the rangeof the salient entities), the correlations were, however, different between the corpora. In Mainichi, the pronominalization ratio smoothly increased through the increase of Pr
in this range. In WSJ, the pronominalization ratio did notincrease in this range, as contrasted with Mainichi.
We investigated this difference between Mainichi and
WSJ in the range of the salient entities. In Mainichi, only
17.6% samples were not pronominalized in that range. In
WSJ, 55.3% (11,367) samples were not pronominalized inthat range as contrasted with Mainichi. By closely investigating, 41.7% (4,735) samples in the non-pronominalized
samples were referenced by the proper nouns in WSJ.
In Japanese, the salient entities are frequently referenced
by the zero pronouns. In English, especially in the newspaper articles, the salient entities are comparatively referenced by the contracted names (e.g., “Dr. Talcott” insteadof “he”) or the definite noun phrases. In this respect, there
is still room for improvement in the definition of perceptual
utility.
5.2. Grounds for the Ut 0 setting
We investigated the influence of Ut 0 , the basic level of
Ut. Figure 4 shows the correlation coefficient between
EU(Ui+1 ) and the transition ranking in Mainichi.
This correlation relates to the consistency of Preference
2 with Rule 2 of CT. 1 The correlation was saturated when
Ut 0 ≥ max I(w) (i.e., Ut(w) ≥ 0 is ensured). How1

Rule 1 of CT does not depend on Ut 0 varying.

We enhanced the design of MGCM in order to establish
a quantitative model adaptable to different language corpora. Two parameters, reference probability and perceptual
utility, should be statistically adapted to various language
corpora. We statistically defined perceptual utility of referential expressions as the load reduction by using the occurrence frequency in the corpus. In this way, we made thetwo parameters adaptable to corpora of various language.
Although the two parameters were distributed differently
between Japanese and English corpora (Tables 4, 5, 7, and8), our definitions of them were valid on both corpora. This
indicates that optimal parameters can be obtained from a
corpus of the target language.
The preferences of MGCM derived from the principleof expected utility were also valid on both corpora. Preferences 1a and 1b related to pronominalization, which
are represented as positive correlations between reference
probability and perceptual utility, were statistically significant. Preference 2 related to transition, which is represented
as the principle of expected utility, was also statistically significant. These results indicate that MGCM and its principle are cross-linguistically valid in Japanese and English.
They also indicate that the expected utility is a valid scaleof referential coherence in Japanese and English.
Therefore, we confirmed that the enhanced MGCM wasadaptable to Japanese and English corpora. Consequently,
we confirmed that the referential coherence of discourse
can be quantitatively measured with the enhanced MGCM
in both Japanese and English. We will try to verify the enhanced MGCM in the other corpora of various languages
or genres.

7.

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